We next seek the solution for \(g\left(u\right)\) . Due to the
randomicity of the wireless channels, we note that \(g(u)\)  has \(N+1\) 
different poles \(z_0=-jm_0/a_0 \) , \(z_1=-jm_1/a_1\) , \(\cdots \) ,
\(z_N=-jm_N/a_N\)  in complex field. As such, based on residue theorem
[1]}, the residue of \(k^{\rm {th}}\)  pole of
\(g(u)\)  in complex field can be expressed as
\({\rm {Res}}\left[{g\left({z_k}\right),z_k}\right]=&\frac{1}{{\left( {m_k - 1} \right)!}}\mathop {\lim }\limits _{u \rightarrow z_k } \frac{{d^{m_k - 1} }}{{du^{m_k - 1} }}\left[ {\left( {u - z_k } \right)^{m_k} g\left( u \right)} \right]\\=&\frac{{{m_k}^{m_k} }}{{(-j)^{m_k} {a_k}^{m_k} \left( {m_k - 1}\right)!}}\mathop {\lim }\limits _{u \rightarrow z_k } \frac{{d^{m_k - 1}}}{{du^{m_k - 1} }}\left[ {e^{ - juv} \left( {\prod \limits _{n = 0,n\ne k}^N {\left( {1 - \frac{{jua_n }}{m_n}} \right)^{ - m_n} } }\right)}\right].\) 
